It is False, they do not have FDA approval . Actually, please see linked letter below from FDA to DoTerra about their "claims" and what their ingredients actually are for. FDA says only use DoTerra if prescribed by a doctor.
I've pulled the most important part out:
"Your products are prescription drugs as defined in section 503(b)(1)(A) of the Act [21 U.S.C. § 353(b)(1)(A)]) for some of the claims made for them because, in light of their toxicity or other potentiality for harmful effect, the method of their use, or the collateral measures necessary to their use, they are not safe for use except under the supervision of a practitioner licensed by law to administer them."
dTERRA International LLC 9 22 14